Méthodes de points intérieurs du type gradient et ε-sous-gradient pour la minimisation avec contrainte convexe

  • Lieve Bonduel

Student thesis: Master typesMaster in Mathematics

Abstract

We extend epsilon-subgradient descent methods for unconstrained nonsmooth convex minimization to constrained problems over polyhedral sets, in particular over Rp+. This is done by replacing the usual squared quadratic regularization term used in subgradient schemes by the logarithmic-quadratic distancelike function. We then obtain ?-subgradient descent methods, which allow us to provide a natural extension of bundle methods and Polyak's subgradient projection methods for nonsmooth convex minimization. Furthermore, similar extensions are considered for smooth constrained minimization to produce interior gradient descent methods.
Date of Award2007
Original languageFrench
SupervisorJean-Jacques Strodiot (Supervisor), Van Hien Nguyen (Jury) & Joseph Winkin (Jury)

Cite this

Méthodes de points intérieurs du type gradient et ε-sous-gradient pour la minimisation avec contrainte convexe
Bonduel, L. (Author). 2007

Student thesis: Master typesMaster in Mathematics